Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
366 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10589572 | C2 | semidirect |
| 5. C9×#339 | C2 | semidirect |
| 6. #10588236 | C2 | semidirect |
| 7. #10588210 | C2 | semidirect |
| 38. C2×D36 | Q8 | semidirect |
| 41. C2×Dic18 | Q8 | semidirect |
| 109. #339 | D9 | semidirect |
| 251. C9 | #2031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589572 | 2 |
| #10588819 | 2 |
| #10588686 | 2 |
| C2×#63364 | 2 |
| C9×#339 | 2 |
| #10588236 | 2 |
| #10588210 | 2 |
| #68779 | 3 |